Alright, this one is going to be a whopper. First let me say that women who are into gaming are more than just a welcome addition to the gamer hordes; women are a big part of that subculture all on their own. The world doesn’t need to “accept” the idea of gamer girls, because the idea is already a solidified reality. The world might as well “accept” the idea of gravity.
Some time ago, when I was introduced to tumblr, I started following the “Gamer Girls” tag. The tag gave me pictures of women holding controllers over their chest, and I sacrificed copies of Duke Nukem Forever in ritual fires to appease it. The relationship was symbiotic at first.